How Association Works

Suppose you are supposed to solve a hard problem. It could be a mathematics problem, a literary problem, a political problem, a family relations problem, or a business problem. Your usual strategy is often to find some similar problem that you know how to solve, and model that solution. But what if this is a new kind of problem, or at least a problem of a sort you don't know how to solve? Problems like this come up all the time in real life as well as school, so let's take a look at how they get solved.

We get ideas for solving problems, so let's look at ideas. We will take a historical approach of how our ideas about ideas appeared. This is a zen exercise: the idea of "ideas" developed historically much as ideas develop in individual people.

You need an idea, so where do ideas come from? There are two schools of thought on this:

• Plato claimed that people have some kind of supernatural access to ideas.
• Aristotle claimed that people observe phenomena, and get ideas from the observations.

One of the most important notions here goes back to the Mystery Religion of Orpheus, in which participants in the mystery religion can gain inspirations from a secret source inaccessible to ordinary people. There were several neo-Orphic organizations, most famously the Pythagorean Order, Plato's school at the grove of Academeus, and the Christian gnostics. All these groups believed in a transcendent world of forms, ideas, etc. that was in a sense more "real" than the physical world around them; the two most famous works advocating this view are Plato's Republic and the Gospel of St. John. This transcendent world is very important to the history of ideas.

While Platonists helped us with a vision of the world of ideas, they were no help at all when it came to figuring out how we got ideas: two thousand years after Plato, the best the great Logician Kurt Gödel could suggest is that we have a sort of sixth sense for (mathematical) ideas: see his Russell's mathematical logic, and What is Cantor's continuum problem. The psychology of ideas has taken a more Aristotilean course. Isaac Newton's contemporary, John Locke, proposed that we take simple ideas and combine them to get more complex ideas. Locke was just getting started, so his kind of example might be something straightforward, like the idea of a paper bag:

• Visually, it is large, brown, rectangular, but open at the top.
• Auditory: it is silent, except when tapped or handled, when it makes a rough sound.
• Tactile: it is relatively but not quite smooth, rigid but not brittle (it bends and gives but springs back).

• It is a flexible surface of five of six sides of a rectangular parallelopiped.

• It is useful for carrying light objects.

In the early Twentieth Century, the man widely regarded as the smartest in the world (Einstein's predecessor) was the mathematician Henri Poincare. Poincare once wrote a description of how he came upon one of this discoveries: he spent a few weeks working on some objects he called "fuchsian functions," trying to figure out what they were. He worked at his study, when, "Ideas rose in crowds; I felt them collide until pairs interlocked, so to speak, making a stable combination." Twice, after getting stuck on the problem working in his study, he took an R & R break, during which he got an idea, and returned to his study and, working out the idea, got major results.

Poincare proposed that in the Unconscious there was an engine that associated many ideas in some labor-intensive fashion until a reasonably good-looking combination was found and triumphantly presented to the Conscious. And many of us have similar experiences: we mull over a problem until, suddenly, it comes to us. Of course, many -- possibly most -- of these ideas merely look good to the Unconscious, but do not stand up to scrutiny (Poincare did not go into this aspect of the phenomenon). Returning to the metaphor of a ship in the Unconscious page, imagine that while physically sitting at in study, your Conscious is the Captain of your mind, which is largely unconscious. The captain badgers the bridge crew (and using the telephone, the engineer and anyone else withing badgering range) into working on the problem; then a number of officers and crew wind up working on the problem (or delegating other crew members -- whom the captain never sees -- into working on the problem) by associating ideas until they get something or several somethings that meet some criteria; they happily present the putatives solutions before the captain who, if he is wise, will check them.

Meanwhile, philosophers imagined that these ideas lived in a world of their own, and they wondered what this world of ideas looked like. One interesting proposal came from the empiricist Karl Popper, who imagined several parallel universes of metaphysical objects, including a "World 3" of Objective Knowledge, inhabited by all the scientific and mathematical facts, and all their combinations. As an example, consider two possible views of this World 3.

• World 3 according to Parmenides and Spinoza. The structures of ideas are eternal, immutable, and perpetually represent the entirety of Truth. Our inability to perceive it in its entirety is merely a reflection of our own mortal limitations.
• World 3 according to Heraclitus and Whitehead. The structures of ideas are transient, changing, and in an everlasting process of resolving situations as they appear. What we see is what is there at that moment.

The more popular view of evolution is teleological, i.e., guided by a purpose, be it an anthropic principle, or the Holy Ghost. The Hindu doctrine of the avatars suggests that evolution has an aim, an aim that is a better or wise world. This view is visible in the work of Friedrich Hegel and Karl Marx. Hegel imagined a process in which there would be two adversarial positions (thesis and antithesis) which would then be resolved (into a synthesis). Hegel lived during the Napoleonic wars, when history seemed guided by ideas, and Hegel imagined a confrontation between systems of ideas, perhaps represented by nations, in a perpetual evolution towards ... towards ... well, paradise, according to Marx. Notice that this view of the world of ideas is teleological, in the sense that it is evolving towards something. This evolution towards something better is one of the most popular images of evolution in general, and spread beyond German idealists and materialists even to inspire Victorians (witness Herbert Spencer --- Mr. "Survival of the Fittest" --- who proposed that the purpose of evolution was to send life towards a higher life form, like the Victorian Englishman) and others (witness Pierre Teilhard de Chardin, who proposed that the evolution of evolution was to evolve from a chaotic Alpha to a complex Omega).

The contrary position is non-teleological, But the Greek Philosopher Anaximander had a very different view: life evolved in reaction to current circumstances. This view has never been as popular, although Darwin's theory of "natural selection" (a more sophisticated variant of Anaximander's position) has persuaded most biologists. Darwin's argument was:

• There is some mechanism within the mechanism of heredity that preserves and mixes the traits of parents to produce offspring, along with some anomalies that those offspring, if they survive, will be able to pass one to their offspring.
• Individuals whose hereditary design works well will likely be successful, and live and thrive and have numerous offspring; those whose hereditary design does not work well will not.
• Thus over time, the design of individuals within a population will adjust to their environment --- their current environment as it is, not their environment to be.

The evolutionary debate also corresponds to a similar debate in the theory of ideas.

"Men come and go," saith the preacher, but "the earth abides." Most primitive societies --- and most of antiquity --- had a cyclical view of time. Day by day, year by year, generation by generation, matters went up and down but, ultimately, were always as they were. Then some Persians developed a linear view of time, of the world slowly becoming better or worse or different; this view of time arrived in Babylon just as Jewish refugees were compiling their oral (and perhaps written) histories into scripture. And those scriptures spread the notion that man makes progress, spiritual, moral, intellectual, perhaps towards some goal, and certainly in some direction. This view tends to be very popular during revolutionary periods, when revolutionaries (like Galileo, Voltaire, Kant, Marx, Huxley, Einstein, etc.) announce that they are dragging society from the benighted past into the enlightened future. (It is also popular among moralists who believe that there is an ideal morality that all people should strive for.) Optimism being popular, many popular books and school texts tended to take such a progressive point of view (see anything by Hendrik van Loon as an example). Associated with these views are the ideas of scientific and artistic progress, that we are developing progressively greater understanding of the universe and of ourselves.

There are, of course, many skeptics about progress, from H. G. Wells, who was gloomy about the future of mankind (this is common among science fiction writers), to contrarians who think that the entire enterprise is a delusion (witness Jacques Derrida, who is not convinced that text, like the material on this web-page, has any meaning independent of the reader). Well, certainly science is as much a human exercise, and a subject of study for psychologists and sociologists. Those who study science and culture, and who ask what are the materials of science and culture wind up with ideas. A skeptic who does not believe in the permanence of ideas may still believe that they are real, it's just that they interact with each other and with the world like anything else, and that leads to different views of ideas. Here are two popular metaphors.

• Memes. Oxford Biologist Richard Dawkins became popular decades ago with his Selfish Gene, in which he claimed that it is useful to imagine that genes, not individuals, are selected in Darwin's natural selection (to which Stephen Jay Gould retorted that it was individuals who lived or died). In that book he proposed a variant of Popper's World 3, inhabited by atomic bits of idea-stuff: phrases, pictoral ideas, scraps of melody, etc. He called these things "memes," and suggested that they tended to survive by collecting in organized structures capable of being transmitted from generation to generation, or culture to culture, much like genes in chromosomes, and hence in populations. The success of a meme depends on what other memes it associates with, and how it associates with them.
• Nuts and bolts. Science writer James Burke wrote an unusual assortment of van Loon-like history books, starting with Connections, in which he described practical ideas as passive objects combined by people in unusual ways to form new things. For example, that old Arab invention, the perfume atomizer, when aimed at something like Alessandro Volta's version of Joseph Priestly's eudiometer -- an air qualiter measuring device involving sparking mechanism -- connecting to another old invention, the piston (first successfully used for power in Thomas Newcomen's external combustion engine), and using Nikolaus Otto's "4 stroke cycle" to synchronize fuel flow and piston movement, the result was Gottlieb Daimler and William Maybech's Mercedes. (Of course, I've left out a lot of details, as, no doubt because of space constraints, did Burke.) This is a more traditional Lockean view of ideas, and Burke is more concerned than Dawkins is with the economic needs and opportunities that generated the inventions. Moreover, Burke's ideas are more mobile than Dawkins' memes: how easily the Arabian atomizer (which can trace its own history to distillation) becomes the heart of the early carburetor.

Thus endeth the zen exercise. You may notice that we still do not know what ideas are, but we do have a better idea of how they behave, and what questions to ask.